The perpendicular bisector of chord AB is y=-2x+8, and the perpendicular bisector of chord BC is y = 3x-2. Recall the properties of chords. How can these equations be used to find the center of the circle that represents the whole plate

We equate the two expressions since they both pass through the center of the circle.

The coordinate of the center of the circle is (2,4)

Step-by-step explanation:

From circle theorem, we know that the perpendicular bisector of a chord passes through the center of the circle.

Since both equations would pass through the center of the circle, we equate them.

So, - 2x+8 = 3x-2

Solving for x, we have

3x + 2x = 8 + 2

5x = 10

x = 10/5

x = 2

Substituting x = 2 into any of the equations, we find the y - coordinate of the center of the circle.

y = - 2x + 8 = - 2 (2) + 8 = - 4 + 8 = 4

So, the coordinate of the center of the circle is (2,4)